Boundary Conditions for 2D Boussinesq-type Wave-Current Interaction Equations

The 2D Incompressible Boussinesq Equations

Damped Wave Equations with Dynamic Boundary Conditions

We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their wellposedness and describe some qualitative properties of their solutions, including boundedness, stability, or almost periodicity. In particular, we are able to characterize the analyticity of ...

Travelling wave solutions to Zufiria’s higher-order Boussinesq type equations

Zufiria’s higher-order Boussinesq type equations are studied by transforming them into solvable ordinary differential equations. Various families of their travelling wave solutions are generated, which include periodic wave, solitary wave, periodic-like wave, solitonlike wave, Jacobi elliptic function periodic wave, combined non-degenerative Jacobi elliptic function-like wave, Weierstrass ellip...

Nearshore Wave Modeling with High-Order Boussinesq-Type Equations

The accuracy of using high-order Boussinesq-type models as compared to the typical order models is examined in this paper. The high-order model used is the two-layer model of Lynett and Liu in 2004, which captures both linear and nonlinear wave evolution up to kh 6. The physical situations examined all involve nearshore breaking, and an eddy-viscosity type breaking model is adopted for the two-...

Initial Boundary Value Problem for 2d Boussinesq Equations with Temperature-dependent Heat Diffusion

We consider the initial-boundary value problem of two-dimensional inviscid heat conductive Boussinesq equations with nonlinear heat diffusion over a bounded domain with smooth boundary. Under slip boundary condition of velocity and the homogeneous Dirichlet boundary condition for temperature, we show that there exists a unique global smooth solution to the initial-boundary value problem for H i...